no. 4
On uniqueness in electromagnetic scattering from biperiodic structures
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 4, pp. 1167-1184.

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.

DOI : 10.1051/m2an/2012063
Classification : 35A02
Mots clés : biperiodic scattering, uniqueness, electromagnetic waves 
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Lechleiter, Armin; Nguyen, Dinh-Liem. On uniqueness in electromagnetic scattering from biperiodic structures. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 4, pp. 1167-1184. doi : 10.1051/m2an/2012063. http://www.numdam.org/articles/10.1051/m2an/2012063/

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